--- a/test/Grids/manifolds_test.jl	Sat Feb 08 09:35:13 2025 +0100
+++ b/test/Grids/manifolds_test.jl	Sat Feb 08 09:38:58 2025 +0100
@@ -4,74 +4,205 @@
 using Diffinitive.RegionIndices
 using Diffinitive.LazyTensors
 
-# using StaticArrays
-
-@testset "ParameterSpace" begin
-    @test ndims(HyperBox([1,1], [2,2])) == 2
-    @test ndims(unittetrahedron()) == 3
-end
-
-@testset "Interval" begin
-    @test Interval <: ParameterSpace{1}
-
-    @test Interval(0,1) isa Interval{Int}
-    @test Interval(0,1.) isa Interval{Float64}
-
-    @test unitinterval() isa Interval{Float64}
-    @test unitinterval() == Interval(0.,1.)
-    @test limits(unitinterval()) == (0.,1.)
-
-    @test unitinterval(Int) isa Interval{Int}
-    @test unitinterval(Int) == Interval(0,1)
-    @test limits(unitinterval(Int)) == (0,1)
-end
-
-@testset "HyperBox" begin
-    @test HyperBox{<:Any, 2} <: ParameterSpace{2}
-    @test HyperBox([1,1], [2,2]) isa HyperBox{Int, 2}
-
-    @test HyperBox([1,2], [1.,2.]) isa HyperBox{Float64,2}
+using StaticArrays
 
-    @test limits(HyperBox([1,2], [3,4])) == ([1,2], [3,4])
-    @test limits(HyperBox([1,2], [3,4]), 1) == (1,3)
-    @test limits(HyperBox([1,2], [3,4]), 2) == (2,4)
-
-    @test unitsquare() isa HyperBox{Float64,2}
-    @test limits(unitsquare()) == ([0,0],[1,1])
-
-    @test unitcube() isa HyperBox{Float64,3}
-    @test limits(unitcube()) == ([0,0,0],[1,1,1])
-
-    @test unithyperbox(4) isa HyperBox{Float64,4}
-    @test limits(unithyperbox(4)) == ([0,0,0,0],[1,1,1,1])
-end
-
-@testset "Simplex" begin
-    @test Simplex{<:Any, 3} <: ParameterSpace{3}
-    @test Simplex([1,2], [3,4]) isa Simplex{Int, 2}
-    @test Simplex([1,2,3], [4,5,6],[1,1,1]) isa Simplex{Int, 3}
-
-    @test Simplex([1,2], [3.,4.]) isa Simplex{Float64, 2}
-
-    @test verticies(Simplex([1,2], [3,4])) == ([1,2], [3,4])
-
-    @test unittriangle() isa Simplex{Float64,2}
-    @test verticies(unittriangle()) == ([0,0], [1,0], [0,1])
-
-    @test unittetrahedron() isa  Simplex{Float64,3}
-    @test verticies(unittetrahedron()) == ([0,0,0], [1,0,0], [0,1,0],[0,0,1])
-
-    @test unitsimplex(4) isa Simplex{Float64,4}
-end
+west = CartesianBoundary{1,LowerBoundary}
+east = CartesianBoundary{1,UpperBoundary}
+south = CartesianBoundary{2,LowerBoundary}
+north = CartesianBoundary{2,UpperBoundary}
+bottom = CartesianBoundary{3, LowerBoundary}
+top = CartesianBoundary{3, UpperBoundary}
 
 @testset "Chart" begin
-    c = Chart(x->2x, unitsquare())
+    X(ξ) = 2ξ
+    Grids.jacobian(::typeof(X), ξ) = @SVector[2,2]
+    c = Chart(X, unitsquare())
     @test c isa Chart{2}
     @test c([3,2]) == [6,4]
     @test parameterspace(c) == unitsquare()
     @test ndims(c) == 2
+
+    @test jacobian(c, [3,2]) == [2,2]
+
+    @test Set(boundary_identifiers(Chart(X,unitsquare()))) == Set([east(),west(),south(),north()])
 end
 
-@testset "Atlas" begin
+@testset "CartesianAtlas" begin
+    @testset "Constructors" begin
+        c = Chart(identity, unitsquare())
+        @test CartesianAtlas([c c; c c]) isa Atlas
+
+        c2 = Chart(x->2x, unitsquare())
+        @test CartesianAtlas([c c2; c2 c]) isa CartesianAtlas
+        @test CartesianAtlas(@SMatrix[c c; c c]) isa CartesianAtlas
+        @test CartesianAtlas(@SMatrix[c c2; c2 c]) isa CartesianAtlas
+    end
+
+    @testset "Getters" begin
+        c = Chart(identity, unitsquare())
+        a = CartesianAtlas([c c; c c])
+        @test charts(a) == [c c; c c]
+    end
+
+    @testset "connections" begin
+        # 2D
+        a = CartesianAtlas(fill(Chart(identity, unitsquare()), 2,3))
+
+        @test Set(connections(a)) == Set([
+            (MultiBlockBoundary{(1,1), east}(), MultiBlockBoundary{(2,1), west}()),
+            (MultiBlockBoundary{(1,1), north}(), MultiBlockBoundary{(1,2), south}()),
+            (MultiBlockBoundary{(2,1), north}(), MultiBlockBoundary{(2,2), south}()),
+            (MultiBlockBoundary{(1,2), east}(), MultiBlockBoundary{(2,2), west}()),
+            (MultiBlockBoundary{(1,2), north}(), MultiBlockBoundary{(1,3), south}()),
+            (MultiBlockBoundary{(2,2), north}(), MultiBlockBoundary{(2,3), south}()),
+            (MultiBlockBoundary{(1,3), east}(), MultiBlockBoundary{(2,3), west}()),
+        ])
+
+        # 3D
+        a = CartesianAtlas(fill(Chart(identity, unitcube()), 2,2,3))
+        @test Set(connections(a)) == Set([
+            (MultiBlockBoundary{(1,1,1), east}(),  MultiBlockBoundary{(2,1,1), west}()),
+            (MultiBlockBoundary{(1,1,1), north}(), MultiBlockBoundary{(1,2,1), south}()),
+            (MultiBlockBoundary{(2,1,1), north}(), MultiBlockBoundary{(2,2,1), south}()),
+            (MultiBlockBoundary{(1,2,1), east}(),  MultiBlockBoundary{(2,2,1), west}()),
+
+            (MultiBlockBoundary{(1,1,2), east}(),  MultiBlockBoundary{(2,1,2), west}()),
+            (MultiBlockBoundary{(1,1,2), north}(), MultiBlockBoundary{(1,2,2), south}()),
+            (MultiBlockBoundary{(2,1,2), north}(), MultiBlockBoundary{(2,2,2), south}()),
+            (MultiBlockBoundary{(1,2,2), east}(),  MultiBlockBoundary{(2,2,2), west}()),
+
+            (MultiBlockBoundary{(1,1,3), east}(),  MultiBlockBoundary{(2,1,3), west}()),
+            (MultiBlockBoundary{(1,1,3), north}(), MultiBlockBoundary{(1,2,3), south}()),
+            (MultiBlockBoundary{(2,1,3), north}(), MultiBlockBoundary{(2,2,3), south}()),
+            (MultiBlockBoundary{(1,2,3), east}(),  MultiBlockBoundary{(2,2,3), west}()),
+
+            (MultiBlockBoundary{(1,1,1), top}(), MultiBlockBoundary{(1,1,2), bottom}()),
+            (MultiBlockBoundary{(2,1,1), top}(), MultiBlockBoundary{(2,1,2), bottom}()),
+            (MultiBlockBoundary{(1,2,1), top}(), MultiBlockBoundary{(1,2,2), bottom}()),
+            (MultiBlockBoundary{(2,2,1), top}(), MultiBlockBoundary{(2,2,2), bottom}()),
+
+            (MultiBlockBoundary{(1,1,2), top}(), MultiBlockBoundary{(1,1,3), bottom}()),
+            (MultiBlockBoundary{(2,1,2), top}(), MultiBlockBoundary{(2,1,3), bottom}()),
+            (MultiBlockBoundary{(1,2,2), top}(), MultiBlockBoundary{(1,2,3), bottom}()),
+            (MultiBlockBoundary{(2,2,2), top}(), MultiBlockBoundary{(2,2,3), bottom}()),
+        ])
+    end
+
+    @testset "boundary_identifiers" begin
+        # 2D
+        a = CartesianAtlas(fill(Chart(identity, unitcube()), 2,3))
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{(1,1), south}(),
+            MultiBlockBoundary{(2,1), south}(),
+            MultiBlockBoundary{(2,1), east}(),
+            MultiBlockBoundary{(2,2), east}(),
+            MultiBlockBoundary{(2,3), east}(),
+            MultiBlockBoundary{(1,3), north}(),
+            MultiBlockBoundary{(2,3), north}(),
+            MultiBlockBoundary{(1,1), west}(),
+            MultiBlockBoundary{(1,2), west}(),
+            MultiBlockBoundary{(1,3), west}(),
+        ])
+
+        # 3D
+        a = CartesianAtlas(fill(Chart(identity, unitsquare()), 2,2,3))
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{(1,1,1), bottom}(),
+            MultiBlockBoundary{(2,1,1), bottom}(),
+            MultiBlockBoundary{(1,2,1), bottom}(),
+            MultiBlockBoundary{(2,2,1), bottom}(),
+
+            MultiBlockBoundary{(1,1,3), top}(),
+            MultiBlockBoundary{(2,1,3), top}(),
+            MultiBlockBoundary{(1,2,3), top}(),
+            MultiBlockBoundary{(2,2,3), top}(),
 
+            MultiBlockBoundary{(1,1,1), west}(),
+            MultiBlockBoundary{(1,2,1), west}(),
+            MultiBlockBoundary{(1,1,2), west}(),
+            MultiBlockBoundary{(1,2,2), west}(),
+            MultiBlockBoundary{(1,1,3), west}(),
+            MultiBlockBoundary{(1,2,3), west}(),
+
+            MultiBlockBoundary{(2,1,1), east}(),
+            MultiBlockBoundary{(2,2,1), east}(),
+            MultiBlockBoundary{(2,1,2), east}(),
+            MultiBlockBoundary{(2,2,2), east}(),
+            MultiBlockBoundary{(2,1,3), east}(),
+            MultiBlockBoundary{(2,2,3), east}(),
+
+            MultiBlockBoundary{(1,1,1), south}(),
+            MultiBlockBoundary{(2,1,1), south}(),
+            MultiBlockBoundary{(1,1,2), south}(),
+            MultiBlockBoundary{(2,1,2), south}(),
+            MultiBlockBoundary{(1,1,3), south}(),
+            MultiBlockBoundary{(2,1,3), south}(),
+
+            MultiBlockBoundary{(1,2,1), north}(),
+            MultiBlockBoundary{(2,2,1), north}(),
+            MultiBlockBoundary{(1,2,2), north}(),
+            MultiBlockBoundary{(2,2,2), north}(),
+            MultiBlockBoundary{(1,2,3), north}(),
+            MultiBlockBoundary{(2,2,3), north}(),
+        ])
+    end
 end
+
+@testset "UnstructuredAtlas" begin
+    @testset "Constructors" begin
+        c1 = Chart(identity, unitsquare())
+        c2 = Chart(x->2x, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        @test UnstructuredAtlas([c1, c1, c1], cn) isa UnstructuredAtlas
+        @test UnstructuredAtlas([c1, c2, c1, c2], cn) isa UnstructuredAtlas
+
+
+        cn = @SVector[
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+        @test UnstructuredAtlas(@SVector[c1, c1, c1], cn) isa UnstructuredAtlas
+        @test UnstructuredAtlas(@SVector[c1, c2, c1, c2], cn) isa UnstructuredAtlas
+    end
+
+    @testset "Getters" begin
+        c = Chart(identity, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        a = UnstructuredAtlas([c, c, c], cn)
+
+        @test charts(a) == [c,c,c]
+        @test connections(a) == cn
+    end
+
+    @testset "boundary_identifiers" begin
+        c = Chart(identity, unitsquare())
+        cn = [
+            (MultiBlockBoundary{1, east}(), MultiBlockBoundary{2, west}()),
+            (MultiBlockBoundary{1, north}(), MultiBlockBoundary{3, west}()),
+            (MultiBlockBoundary{2, north}(),  MultiBlockBoundary{3, south}()),
+        ]
+
+        a = UnstructuredAtlas([c, c, c], cn)
+
+        @test Set(boundary_identifiers(a)) == Set([
+            MultiBlockBoundary{1, west}(),
+            MultiBlockBoundary{1, south}(),
+            MultiBlockBoundary{2, south}(),
+            MultiBlockBoundary{2, east}(),
+            MultiBlockBoundary{3, north}(),
+            MultiBlockBoundary{3, east}(),
+        ])
+
+    end
+end